Magnesite Enstatite Forsterite CO2 in the Ranges 6–25 Kbar and 700

American Mineralogist, Volume 83, pages 213±219, 1998

؍ Experimental determination of the reaction: Magnesite ؉ enstatite forsterite ؉ CO2 in the ranges 6±25 kbar and 700±1100 ؇C

ANDREA M. KOZIOL1 AND ROBERT C. NEWTON2

1Department of Geology, University of Dayton, Dayton, Ohio 45469-2364, U.S.A. 2Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois 60637, U.S.A.

ABSTRACT

The P-T equilibrium curve of the reaction of magnesite ϩ enstatite ϭ forsterite and CO2 was determined in the ranges 6±25 kbar and 700±1100 ЊC by 53 reversed experiments carried out in 1.91 cm diameter piston-cylinder apparatus with NaCl pressure medium.

Silver oxalate was used as a CO2 source and charges were buffered at hematite-magnetite oxygen fugacity. Reaction progress was monitored by weight changes upon puncturing of

CO2-in¯ated quenched charge capsules and was con®rmed by comparing X-ray diffrac- tograms of charges made before and after the experiments. The data satisfy the relation: Ϫ3 Ϫ5 2 PEQ ϭϪ3.215 Ϫ 4.784 ϫ 10 T ϩ 2.542 ϫ 10 T with P in kbar and T in ЊC. A P-T curve calculated with the 1994 version 2.3 THERMOCALC program agrees well with our results except in the highest pressure range. Our data, together with three existing tight

experimental brackets on the decarbonation reaction of magnesite to periclase and CO2, 0 give ⌬H f (298 K) (forsterite) ϭϪ61.20 Ϯ 0.87 kJ/mol from the oxides. This value is in agreement with the value adopted by Berman (1988). An analysis of various proposed

equations of state for CO2 shows that only those of MaÈder and Berman (1991) and Frost and Wood (1997) meet the constraints imposed by this study near 1000 ЊC and 10±20

kbar. The modi®ed Redlich-Kwong (MRK)-based equations of state overestimate CO2 fugacity in this pressure range.

INTRODUCTION This study presents the results of piston-cylinder ex- Carbonate minerals may be the major reservoir for C periments on reaction 1 conducted over a broad temper- in the mantle and therefore may play an important role ature-pressure range, 700 to 1100 ЊC and 6 to 25 kbar. This range bridges the gap between the previous high- in the global carbon cycle. The system MgO-SiO2-CO2 provides a simple chemical model for understanding the pressure study of Newton and Sharp (1975) and the 2 relationship between silicate, carbonate, and reduced car- kbar work of Johannes (1969). Analysis of our data along bon phases in the mantle. Mg-rich olivine and orthopy- with results on the reaction magnesite ϭ periclase ϩ CO2 roxene are the major minerals of mantle peridotites, and (Johannes and Metz 1968; Koziol and Newton 1995) magnesite is a stable carbonate at mantle pressures great- leads to an improved value for the enthalpy of formation er than about 3.5 GPa (Brey et al. 1983; Kushiro et al. of forsterite. In addition, because reaction 1 is tightly 1975). Magnesite has been shown to be in equilibrium bracketed by our experiments from 6±25 kbar, we can place limitations on the fugacity of CO2 in this pressure- with (Mg,Fe)SiO3 perovskite and magnesiowuÈstite at 50 GPa and 1500±2500 K (Biellman et al. 1993), and it also temperature range and evaluate several published CO2 has been noted, though rarely, as an inclusion in diamond equations of state. (Wang et al. 1996). The most important equilibrium governing the stability EXPERIMENTAL METHODS of magnesite in the Earth's mantle is Experiments on reaction 1 were made using procedures similar to those described in Koziol and Newton (1995). MgSiO ϩ MgCO ϭ Mg SiO ϩ CO . (1) 33242 The experiments were carried out in two different piston- enstatite magnesite forsterite cylinder apparatus with slightly different designs and ca- Normal upper mantle geothermal gradients lie well within pabilities. All experiments were made under piston-out the stability ®eld of the left-hand assemblage; decarbon- conditions. A press engineered for moderate pressures, ation may occur in mantle regions of abnormally high referred to here as BG, was used for experiments at 6.5 temperatures (Eggler et al. 1979; Newton and Sharp to 15.5 kbar. Calibration experiments showed that no fric- 1975). However, modeling the role of decarbonation re- tional pressure correction is required and that maximum actions in the mantle requires an equation of state for CO2 pressure uncertainties are Ϯ200 bars. Another press, en- that is accurate at mantle pressure-temperature conditions. gineered for higher pressure conditions and referred to 0003±004X/98/0304±0213$05.00 213 214 KOZIOL AND NEWTON: STABILITY OF ENSTATITE AND MAGNESITE

TABLE 1. Reversed experiments on the reaction magnesite ϩ obtained for the BB press by Jenkins et al. (1985) and enstatite ϭ forsterite ϩ CO2 (reaction 1) Koziol and Newton (1988). Pressures reported in this pa- Expect- Actual per are nominal pressures.

ed CO2 CO2 Reaction Samples consisted of homogenized powders of syn- Expt. Press T P Time loss loss direction thetic enstatite, synthetic magnesite, and synthetic for- no. used (ЊC) (kbar) (h) (mg) (mg) by XRD sterite, sealed in 1 mm diameter platinum tube segments 5.154 BG 712 6.5 145 1.12 0.84 magn ϩ en with weighed amounts of silver oxalate (Ag C O )asthe 5.135 BG 712 7.1 99 1.13 0.56 magn ϩ en 2 2 4 MEF-11 BG 720 6.5 168 1.09 1.08 no reaction CO2 source. Synthetic forsterite was prepared from a thor-

5.148 BG 722 7.0 118 1.19 1.01 magn ϩ en oughly homogenized stoichiometric mix of ultrapure SiO2 MEF-13 BG 725 6.5 169 0.82 1.01 fo ϩ CO2 5.143 BG 732 6.9 119 1.14 1.24 no reaction glass and synthetic magnesite. The mix was decarbonated 5.151 BG 737 6.9 116 1.10 1.13 no reaction in a platinum crucible at 800 ЊC and then sintered at about MEF-12 BG 740 7.0 266 0.89 1.14 fo ϩ CO2 1200 ЊC for 3 d. The material was ®nely ground, pel- 5.121 BG 742 8.5 88 1.07 0.84 magn en ϩ letized, and recycled at approximately 1400 ЊCfor2d. 5.122 BG 750 6.7 142 1.16 1.50 fo ϩ CO2 5.146* BG 750 8.1 118 Ð Ð magn ϩ en The resulting material was 99% forsterite, with a very MEF-5 BG 755 8.0 148 0.84 0.64 magn ϩ en small amount of protoenstatite, as shown by optical ex- 5.128 BG 757 8.1 120 0.97 1.12 no reaction MEF-6 BG 760 8.0 144 1.15 1.04 magn ϩ en amination and X-ray diffraction. Unit-cell dimensions of MEF-3 BG 765 8.0 150 1.59 1.83 fo ϩ CO2 the forsterite determined by X-ray scans with an internal MEF-4 BG 774 8.0 124 1.22 1.61 fo ϩ CO 2 standard, are (in angstroms): a ϭ 4.752(1), b ϭ 10.200(2), MEF-2 BG 780 8.0 146 0.86 1.09 fo ϩ CO2

5.119 BG 782 8.0 96 1.09 1.44 fo ϩ CO2 and c ϭ 5.984(1). Preparation of other materials is dis- MEF-1 BG 800 8.0 165 1.31 1.71 fo ϩ CO2 cussed in Koziol and Newton (1995). 5.118 BG 801 10.0 70 1.12 0.82 magn ϩ en 5.133 BG 812 10.2 73 1.10 0.77 magn ϩ en All experiments were conducted with a hematite-mag- 5.138 BG 815 10.0 119 1.16 0.75 magn ϩ en netite buffer consisting of 35±50 mg sintered reagent he- 5.123 BG 822 10.2 120 1.10 0.97 magn ϩ en matite and 5±10 mg of H O sealed with the platinum MEF-7 BG 825 10.0 73 1.07 1.21 fo ϩ CO 2 2 capsule ina3mmdiameter gold tube segment of 0.15 5.116 BG 832 10.1 73 0.976 1.17 fo ϩ CO2 5.120 BG 842 10.0 93 1.17 1.41 fo ϩ CO2 mm wall thickness. Magnetite formed from this mixture 5.129 BG 842 10.2 17 1.07 1.08 no reaction very quickly at the temperatures and pressures of the ex- MEF-10 BG 850 12.0 71 0.81 0.41 magn ϩ en

MEF-9 BG 870 12.0 72 1.17 1.43 fo ϩ CO2 periments. Experiments were considered well-buffered if MEF-8 BG 880 12.0 69 1.2 1.46 fo ϩ CO2 no weight loss of the gold capsule was detected and if 5.126 BG 914 14.1 16 1.13 1.02 magn ϩ en 5.141 BG 923 14.0 68 1.07 0.78 magn ϩ en the presence of both magnetite and hematite was con- 5.131 BG 928 14.1 24 1.17 1.02 magn ϩ en ®rmed in the buffer product. 5.127 BG 951 14.2 20 1.19 2.03 fo ϩ CO 2 Two methods were used to monitor reaction direction. 5.130 BG 955 15.5 14 1.10 0.54 magn ϩ en 5.140 BB 963 16.2 7 1.15 0.75 magn ϩ en Powder X-ray diffractometer scans of the same charges 5.142 BB 983 16.3 6.5 1.17 0.70 magn ϩ en obtained before and after the experiments were compared. 5.136 BB 984 18.3 18 1.14 0.57 magn ϩ en In addition, weight loss upon puncturing of the sample 5.137 BB 993 16.4 25 1.10 1.95 fo ϩ CO2 5.139 BB 1005 18.3 20 1.07 0.66 magn ϩ en capsule was recorded. Details of the weighing technique

5.152 BB 1006 15.9 46 1.18 2.02 fo ϩ CO2 used are in Koziol and Newton (1995). A CO2 yield larger 5.134 BB 1020 18.3 14 1.13 1.44 fo ϩ CO2 5.145 BB 1022 18.6 24 1.14 0.85 magn ϩ en than expected from the Ag2C2O4 decomposition indicated 5.144 BB 1023 18.5 1 1.07 1.41 no reaction reaction to forsterite ϩ CO2 whereas a CO2 yield smaller 5.132 BB 1044 18.5 22 1.11 1.99 fo ϩ CO2 5.147 BB 1044 20.3 42 1.10 0.47 magn ϩ en than expected signi®ed magnesite growth. Final CO2

5.150 BB 1063 20.0 49 1.19 1.91 fo ϩ CO2 amounts either 20% more or 20% less by weight were 5.153 BB 1065 21.8 42 1.03 0.45 magn ϩ en considered signi®cant. X-ray diffraction scans were ex- 5.149 BB 1082 20.1 44 1.13 1.73 fo ϩ CO2 5.155 BB 1084 22.4 43 1.10 0.58 magn ϩ en amined for relative increase or decrease in strength of

5.158 BB 1100 22.3 43 1.14 1.78 fo ϩ CO2 forsterite re¯ections and corresponding decrease or in- 5.159 BB 1113 24.2 20 1.18 0.51 magn ϩ en crease in strength of enstatite and magnesite re¯ections. 5.160 BB 1131 24.3 22 1.07 0.38 magn ϩ en

Note: The column ``Reaction Direction by XRD'' lists results of our anal- RESULTS OF EXPERIMENTS ysis of the solid experimental product. Analysis of the CO2 weight loss data is discussed in the text. In all cases reaction direction as judged by Character of reaction CO2 loss is the same as that judged by XRD analysis. * Capsule in experiment 5.146 was inadvertently pierced before weigh- Experiments on reaction 1 are listed in Table 1 and ing and no weight-loss data could be collected. shown in Figure 1. These include all experiments in which the inner and outer capsules maintained constant mass. In most experiments a de®nite indication of reac- here as BB, was used for experiments at 16 to 24.5 kbar. tion direction by volatile weight loss was con®rmed by All operating parameters such as pressure medium, ther- X-ray diffraction. A few experiments in which neither mocouples, etc., were the same as for the low-pressure volatile nor change in X-ray re¯ection intensity was sig- experiments. The BB press was calibrated against various ni®cant are tabulated as ``no reaction.'' ®xed points in the range 800 to 900 ЊC, which indicated No new phases other than silver from the decarbona- a pressure correction of Ϫ200 bars. Similar results were tion of Ag2C2O4 were detected optically or with X-ray KOZIOL AND NEWTON: STABILITY OF ENSTATITE AND MAGNESITE 215 analysis. A darker charge occasionally resulted when all of the Ag2C2O4 was loaded in one place in a capsule. This darkening might be due to small amounts of graphite. However, graphite was never identi®ed on the X-ray diffraction scans, so we cannot con®rm its presence. It was found that loading the Ag2C2O4 in increments interspersed with the reaction mix yielded snow-white charges. We were unable to detect any systematic perturbation of the experimental results coincident with darker color of the charges.

Purity of the CO2 ¯uid phase during the experiments is a critical issue. Calculations using the THERMOCALC version 2.3 program of Holland and Powell (1990) indi- cate that at our experimental conditions a 10% reduction in CO2 fugacity lowers the apparent position of reaction

1by10±15ЊC. It is possible that amounts of H2O too small to detect by our drying and weight-loss technique FIGURE 1. All reversal experiments of the present study on could have entered the experimental charges either by H2 the reaction magnesite ϩ enstatite ϭ forsterite ϩ CO2 (reaction in®ltration during the experiments, by adsorbed H2Oin the starting mineral mix, or from the silver oxalate. The 1). Open symbols ϭ growth of magnesite and enstatite. Filled symbols ϭ growth of forsterite and CO2. Half-®lled symbols ϭ ®rst two sources are unlikely because of the highly oxi- no reaction. Experimental uncertainties are the size of the sym- dizing buffer used and the stringent drying procedures bols. Also plotted is a hand-®tted curve to the equilibrium that before sealing of the capsules. Weight loss tests by Koziol Ϫ3 obeys the equation PEQ ϭϪ3.215 Ϫ 4.784 ϫ 10 T ϩ 2.542 Ϫ5 2 and Newton (1995) indicated that the Ag2C2O4 used both ϫ10 T , with T in ЊC and P in kbar. in that study and the present study produced effectively pure CO2 upon decarbonation. If CO were present in our quenched experimental a mathematical ®t to the midpoints of the experimental charges, it would not be detected by our weight loss tech- brackets. The hand-drawn curve was modeled with a nique. Rosenbaum and Slagel (1995) noted that pure CO2 polynomial expression: was produced from silver oxalate using a double capsule P ϭϪ3.215 Ϫ 4.784 ϫ 10Ϫ3 T ϩ 2.542 ϫ 10Ϫ5 T 2 method similar to ours. However, in one piston-cylinder EQ experiment carried out at 800 ЊC and 8 kbar, they ob- with P in kbar and T in ЊC. This function is valid in the served that the mole fractions of CO2,H2O, and CO in pressure range 6±25 kbar and satis®es all of the experi- the ¯uid were 0.90, 0.08, and 0.02, respectively. mental brackets with the exception of one datum at 983 To investigate the integrity of our procedure, two de- ЊC and 16.3 kbar (experiment no. 5.142, Table 1). ®nitive experiments at 10 kbar, 830 and 825 ЊC, were repeated without any silver oxalate added to the sample Comparison with previous results capsule. Both experiments resulted in complete reaction In the MgO-SiO2ϪCO2 system, equilibrium 1 and the to forsterite ϩ CO2 after 4 d. The quenched platinum carbonation-decarbonation reactions: capsules were in¯ated with CO . There was no drying 2 MgCO ϭ MgO ϩ CO (2) loss of the punctured capsules after heating at 320 ЊC for 32 magnesite periclase 20 min. If our earlier experiments had been displaced by signi®cant quantities of H2O or CO, then these experi- and ments should have indicated the stability of magnesite MgCO32ϩ SiO ϭ MgSiO 32ϩ CO (3) and enstatite. It is concluded that any H2O introduced in the silver oxalate had no signi®cant effect on our decar- magnesite quartz enstatite bonation experiments. have been determined by several experimental studies. Newton and Sharp (1975) found a slight increase of For reaction 2, the two brackets of Johannes and Metz the unit-cell parameters of magnesite quenched from an (1968), 705 Ϯ 5 ЊC at 500 bars, and 765 Ϯ 5 ЊC at 1000 experiment conducted at 1450 ЊC and 41.5 kbar. We ex- bars, appear to be de®nitive. Koziol and Newton (1995) amined the strong (104) peak of magnesite from our high- produced an additional bracket at 715 ЊC, 590 Ϯ 30 bars. est temperature experiments with X-ray diffraction at ⅛Њ/ The brackets of Harker and Tuttle (1955) are too broad min using the nearby (610) peak of enstatite as an internal for our analysis and the experiments of Irving and Wyllie standard. No change of the position of the magnesite peak (1975) were performed at conditions outside our study. was evident, indicating that no quenchable changes occur Recent experimental work by Koziol and Newton (1995) in magnesite over the present experimental conditions. determined reaction 3 from 640 to 900 ЊC in the pressure The data plotted in Figure 1 were ®tted by hand. Sev- range 7.5 to 18 kbar. eral ®tting trials yielded virtually identical curves, as did Johannes (1969) was able to place constraints on re- 216 KOZIOL AND NEWTON: STABILITY OF ENSTATITE AND MAGNESITE

sealed platinum capsules that allowed escape of CO2 when decarbonation occurred. Eggler et al. (1979) used sealed platinum capsules that held either forsterite and

Ag2C2O4 or a mixture of magnesite, MgO, and SiO2. None of these studies were done with oxygen fugacity buffers

to eliminate the possibility of H2 in®ltration during the experiments. No study has demonstrated whether, when the same starting mineral mixture was used, the direction of reaction 1 was reversed by changing the experimental pressure or temperature. Only two previous experimental brackets, those of Newton and Sharp (1975) at 19 kbar and 23.7 kbar, lie within the pressure range of the present study (Fig. 2). Their brackets agree quite well with the present determinations, considering the large pressure uncertainties (Ϯ 1.5 kbar) associated with the use of talc-glass pressure media in these earlier experiments. A P-T equilibrium curve of reaction 1 was calculated with version 2.3 of THERMOCALC based on the data set of Holland and Powell (1990), with an equation of

state for CO2 similar in form to that of Holland and Pow- FIGURE 2. Present reversals of reaction 1 compared with un- ell (1991). For comparison, the position of this equilib- reversed experimental data of Newton and Sharp (1975) and Jo- rium calculated by MaÈder and Berman (1991) is also plot- hannes (1969 ϭ Half-bracket in forsterite ϩ CO2 ®eld). Open ted. The curves, shown in Figure 2, agree quite well with symbols ϭ growth of magnesite and enstatite. Filled symbols ϭ our experimental brackets, except for slight divergence growth of forsterite and CO . Solid curve ϭ position of reaction 2 by the Holland and Powell (1990) curve to lower pres- 1 calculated from the Holland and Powell THERMOCALC (ver- sures in the highest temperature range. Both curves pro- sion 2.3) computer program. Dashed curve ϭ position of reaction 1 as calculated by MaÈder and Berman (1991). vide a consistent extrapolation to lower temperatures and pressures and pass very close to the projected point at 2 kbar and 558 ЊC of Johannes (1969). action 1 with several experiments in the MgO-SiO -H O- 2 2 DISCUSSION CO2 system. In hydrothermal experiments conducted at 2 kbar and 560±565 ЊC, a mixture of crystalline enstatite, Enthalpy of formation of forsterite 0 magnesite, and a small amount of H2O reacted to form A value of the enthalpy of formation (⌬H f ) of forsterite forsterite and a ¯uid containing 95±98 mol% CO2.A was derived from the present data, the experimental re- short projection to pure CO2 placed reaction 1 at 558 ЊC sults for reaction 3 of Koziol and Newton (1995), and the at 2 kbar. three existing tight brackets for reaction 2. Supporting Numerous experimental brackets on reaction 1 at pres- data, given in Table 2, include measured low-temperature sures above 19 kbar have been determined in solid pres- and high-temperature heat capacities. Heat capacities of sure media apparatus (Eggler et al. 1979; Haselton et al. all the phases except magnesite were determined calori- 1978; Newton and Sharp 1975) The latter two studies metrically in the temperature range of the calculations; used starting mixtures of enstatite and magnesite in un- magnesite heat capacity has been measured only up to

TABLE 2. Thermodynamic data and sources relevant to derivations in the text

␤V ϫ Њ Њ 3 Ϫ4 5 5 6 Phase ⌬H f298 S 298 abϫ 10 c ϫ 10 d ϫ 10 e V298 ␣V ϫ 10 10 Ref. Forsterite Ϫ61.20 94.11 87.36 87.17 Ϫ369.9 Ϫ2.237 843.6 4.366 16.0 3.2 1, 2, 3

Mg2SiO4 Ϯ0.87 Enstatite Ϫ33.41 66.27 350.7 Ϫ147.3 167.9 5.826 Ϫ4296.0 3.131 9.0 2.3 3, 4, 5

MgSiO3 Ϯ0.83 Magnesite Ϫ116.83 65.09 81.12 52.25 Ϫ183.20 0 0 2.803 12.7 2.6 3, 4, 6*

MgCO3 Ϯ0.47 Periclase 0 26.94 65.211 Ϫ1.270 Ϫ46.185 0 Ϫ387.24 1.125 4.6 0.7 6, 3

CO2 0 213.79 87.82 Ϫ2.644 70.641 0 Ϫ998.86 6 Note: Values for enthalpy (H), entropy (S), heat capacity coef®cients (a±e), volume, expansivity (␣V), and compressibility (␤V) are in J, K, bar. Heat Ϫ2 2 Ϫ1/2 Њ capacity: CP ϭ a ϩ bT ϩ cT ϩ dT ϩ eT . Speci®c volume: V(T,P) ϭ V 298 ϩ (T Ϫ 298)(␣V) Ϫ P(␤V). References: 1 ϭ Present study; 2 ϭ Robie et al. (1982); 3 ϭ Holland and Powell (1990); 4 ϭ Koziol and Newton (1995); 5 ϭ Krupka et al. (1985a, 1985b); 6 ϭ Robie et al. (1978). The ␣V and ␤V values for magnesite agree with Zhang et al. (1997). * Magnesite heat capacity coef®cients are the extrapolation of ref. 6. KOZIOL AND NEWTON: STABILITY OF ENSTATITE AND MAGNESITE 217

TABLE 3. Enthalpy of formation of forsterite derived from experimental data

Њ Њ T P1 ¦CO2 P2 ¦CO2 ⌬H f Fo ⌬H f Fo Њ (ЊC) (kbar) (reaction 1) (kbar) (reaction 2) ⌬H 4 (oxides) (elements) 705 6.05 47.88 0.50 0.55 Ϫ27.79 Ϫ61.20 Ϫ2174.82 715 6.36 55.50 0.59 0.67 Ϫ27.54 Ϫ60.95 Ϫ2174.57 765 8.00 112.17 1.00 1.28 Ϫ28.04 Ϫ61.45 Ϫ2175.07 Average Ϫ61.20(87) Ϫ2174.82(99)

Note: Fugacity and enthalpy values are in kJ/mol. Enthalpy values are at 1 bar, 298 K. CO2 fugacity from Shmulovich and Schmonov (1978). P1 is the pressure of reaction 1 (enstatite ϩ magnesite ϭ forsterite ϩ CO2) at the given T. P2 is the pressure of reaction 2 (magnesite ϩ quartz ϭ enstatite

ϩ CO2) at the given T. Equilibrium pressures for reaction 1 from present work; for reaction 2 from Johannes and Metz (1968) and Koziol and Newton Њ (1995). The ⌬H 4 value is the enthalpy change of reaction 4 (enstatite ϩ periclase ϭ forsterite).

750 K, but magnesite is eliminated between reactions 1 perature range between the direct PVT measurements of and 2 in the derivation given below. The three de®nitive CO2 volumes at low pressures and the previous studies brackets of reaction 2 were performed in gas-pressure on reaction 1 at high pressures. The position of this re- vessels under closely controlled P-T conditions, with reaction in terms of pressure and temperature is constrained versal of the equilibrium. This allows for three precise more stringently by reversed experiments than in previous 0 calculations of ⌬H f of forsterite. CO2 is also eliminated studies. between reactions 1 and 2 at each temperature to yield Calculation of ⌬G0 of reaction 1 can be used to derive reaction 4: the fugacity of CO2 and evaluate the various equations of state. We use the expression MgO ϩ MgSiO324ϭ Mg SiO . (4) periclase enstatite forsterite 0 ⌬G ϭϪP⌬V* Ϫ RT ln ¦CO2 (5)

0 0 The three values of ⌬H f of forsterite from the oxides at where ⌬G is the free energy change of reaction 1 at 1

298 K, together with the CO2 fugacity data necessary for bar and the temperature of interest, P is the equilibrium the calculation, are given in Table 3. Our average value pressure of reaction 1 at that temperature, and ⌬V* is the is Ϫ61.20 Ϯ 0.87 kJ from the oxides (Ϫ2174.72 kJ from characteristic solid volume change evaluated at T and the elements). The calculation relies on the value of P/2. Volume and thermal expansion and isothermal com- 0 ⌬H f of enstatite of Ϫ33.41 Ϯ 0.83 kJ at 298 K of Koziol pressibility coef®cients are generally well-known and un- and Newton (1995). Using the heat capacity coef®cients certainties due to less reliable thermodynamic data are for forsterite of Gillet et al. (1991) makes no signi®cant eliminated, in particular the uncertain heat capacity of 0 difference in the calculation. Our value of ⌬H f agrees magnesite at elevated temperatures. Our tight experimen- closely with that adopted by Berman (1988: Ϫ2174.42 kJ tal brackets allow us to evaluate ⌬G0 at 700, 750, 800, from the elements) but less well with that used by Hol- and 850 ЊC using volume data from Table 2 and the tab- land and Powell (1990: Ϫ2171.87 Ϯ 1.62 kJ). Our value ulated CO2 fugacities of Shmulovich and Shmonov 0 for ⌬H f of forsterite and the data in Table 2 lead to an (1978) (see Table 4). The data of Zhang et al. (1997) were equilibrium temperature of reaction 1 of 547 ЊC at 2 kbar, used to derive values for the thermal expansion and iso- slightly lower than the projection of Johannes (1969). thermal compressibility of magnesite. The ⌬G0 is a reg- ularly varying function of temperature that can be ex- CO2 fugacity at mantle conditions trapolated with small uncertainty to 1000 ЊC. At this Previous experimental determinations of reaction 1 temperature reaction 1 is in equilibrium at 17.4 kbar. Our (Eggler et al. 1979; Haselton et al. 1978; Newton and conservative estimate of the uncertainty in ⌬G0 is based Sharp 1975) have been used by various workers to eval- in part upon a 2% uncertainty in ⌬V*, which includes the uate their CO2 equation of state (Frost and Wood 1997; range in calculated volumes from various data sets. In

Holland and Powell 1991; MaÈder and Berman 1991). addition, we estimate the uncertainty in RT ln ¦CO2 at 10 These different equations of state are not compared easily kbar and 1000 ЊC from Shmulovich and Shmonov (1978) because each study used different tabulated thermody- to be Ϯ1300 J. This value embraces all of the estimates namic properties of forsterite, enstatite, and magnesite, in of RT ln ¦CO2 from various published equations of state. 0 addition to different formulations of CO2 volume and fu- Calculations using the ⌬H f and heat capacity data in Ta- gacity data. Each study also incorporated different im- ble 2 also predict a reasonable value of ⌬G0 at 1000 ЊC portant assumptions, for example, the form of the extrap- (see Table 4), as do calculations using THERMOCALC olation of the heat capacity of magnesite to temperatures version 2.3 (Holland and Powell 1990) and the Berman above 750 K. (1988) data set with updates and CO2 fugacities as de- Our determination of the equilibrium magnesite ϩ en- scribed in MaÈder and Berman (1991), even though values 0 statite ϭ forsterite ϩ CO2 (reaction 1) provides a further of ⌬H f for the solids in the Holland and Powell and MaÈd- test of literature models of the equation of state of CO2. er and Berman data sets are different.

Our experimental results are in a critical pressure-tem- At pressures above 15 kbar the various CO2 equations 218 KOZIOL AND NEWTON: STABILITY OF ENSTATITE AND MAGNESITE

TABLE 4. Thermodynamic parameters of the reaction magnesite ϩ enstatite ϭ forsterite ϩ CO2 derived from the present experimental data

Ϫ⌬G Њ (kJ)

T P RT ln ¦CO2 Ϫ⌬V* MaÈder & Holland & (ЊC) (kbar) (kJ) (J/bar) Experimental Table 2 Berman 91 Powell 700 5.89 86.58 1.602 77.14 77.35 750 7.5 97.17 1.603 85.15 85.27 800 9.23 107.83 1.604 93.03 93.12 850 11.09 118.57² 1.606 100.76 100.89 1000 17.42 151.14 1.609 (123.11) 123.67 123.19 124.13 Ϯ1.42 Ϯ1.34

Note: RT in ¦CO2 values from Shmulovich and Shmonov (1978). The Ϫ⌬G Њ experimental is derived from the relationship ⌬G ЊϭϪP⌬V * Ϫ RT ln

¦CO2 (see text). The value in parentheses is an extrapolation which allows for the apparent decrease of ͦ⌬G Њͦ with T. The Ϫ⌬G Њ of Table 2 is calculated using data in Table 2. RT ln ¦CO2 at 1000 ЊC and 17.42 kbar of 151.14 kJ is consistent with our experimental ⌬G Њ. Holland & Powell value calculated using version 2.3 (1994) of THERMOCALC. *⌬V* (solid volume change evaluated at T and P/2) calculated from data in Table 2. ² Denotes short extrapolation. of state (Bottinga and Richet 1981; Frost and Wood 1997; experimentally determined position of reaction 1 is neg- Holland and Powell 1991; Kerrick and Jacobs 1981; ligible. The equations of state of MaÈder and Berman MaÈder and Berman 1991; Saxena and Fei 1987; Sterner (1991) and Frost and Wood (1997) ®t the constraint cal- and Pitzer 1994) start to diverge in their estimates of vol- culated from our experimental data but the other models ume and fugacity, and our data may be used to discrim- either over- or under-estimate ln ␥CO2 with the MRK mod- inate among them. This is shown in Figure 3, which is els in particular tending toward over-estimation. Kerrick an isothermal plot of ln ␥CO2 vs. pressure at 1000 ЊC. The and Jacobs (1981) note that their formulation may not be bracket at 17.4 kbar is derived from the calculations de- reliably extrapolated to pressure approaching 20 kbar. scribed above and based on data in Table 4. Uncertainty Further work on the enstatite-magnesite-forsterite-CO2 in our calculated value of ln ␥CO2 due to uncertainty in the equilibria or related equilibria will aid in the analysis of

published equations of state for CO2.

ACKNOWLEDGMENTS This research was supported by National Science Foundation grant no. EAR-9310264. Additional support was provided by a University of Day- ton Research Institute seed grant to Andrea Koziol. We thank Volkmar Trommsdorff for helpful discussions and K. Hagan for help in assessing X-ray diffraction data. Critical comments by J.A.D. Connolly, J.G. Liou, and D.M. Jenkins improved the paper.

REFERENCES CITED Berman, R.G. (1988) Internally consistent thermodynamic data for min-

erals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-

H2O-CO2. Journal of Petrology, 29, 445±522. Biellman, C., Gillet, P., Guyot, F., Peyronneau, J., and Reynard, B. (1993) Experimental evidence for carbonate stability in the Earth's lower mantle. Earth and Planetary Science Letters, 118, 31±41. Bottinga, Y. and Richet, P. (1981) High pressure and temperature equation of state and calculation of the thermodynamic properties of gaseous carbon dioxide. American Journal of Science, 281, 615±660. Brey, G., Brice, W.R., Ellis, D.J., Green, D.H., and Harris, K.L. (1983) Pyroxene-carbonate reactions in the upper mantle. Earth and Planetary Science Letters, 62, 63±74. Eggler, D.H., Kushiro, I., and Holloway, J.R. (1979) Free energies of decarbonation reactions at mantle pressures: I. Stability of the assemblage

forsterite-enstatite-magnesite in the system MgO-SiO2-CO2-H2Oto60 kbar. American Mineralogist, 64, 288±293. Frost, D.J. and Wood, B.J. (1997) Experimental measurements of the fu-

gacity of CO2 and graphite/diamond stability from 35 to 77 kbar at 925 FIGURE 3. Isothermal plot of ln as calculated by various to 1650 ЊC. Geochimica et Cosmochimica Acta, 61, 1565±1574. ␥CO2 equations of state against pressure. The bracket at 17.4 kbar is Gillet, P., Richet, P., Guyot, F., and Fiquet, G. (1991) High-temperature thermodynamic properties of forsterite. Journal of Geophysical Re- calculated from our data as described in the text. KJ ϭ Kerrick search, 96, 11805±11816. and Jacobs (1981); BR ϭ Bottinga and Richet (1981); SP ϭ Harker, R.I. and Tuttle, O.F. (1955) Studies in the system CaO-MgO-CO2: Sterner and Pitzer (1994); HP ϭ Holland and Powell (1991); MB I. The thermal dissociation of calcite, dolomite and magnesite. Ameri- ϭ MaÈder and Berman (1991); FW ϭ Frost and Wood (1997); can Journal of Science, 253, 209±224.

SF ϭ Saxena and Fei (1987). Haselton, H.T.J., Sharp, W.E., and Newton, R.C. (1978) CO2 fugacity at KOZIOL AND NEWTON: STABILITY OF ENSTATITE AND MAGNESITE 219

high temperatures and pressures from experimental decarbonation re- properties of anthophyllite, diopside, enstatite, bronzite, and wollasto- actions. Geophysical Research Letters, 5, 753±756. nite. American Mineralogist, 70, 249±260. Holland, T.J.B. and Powell, R. (1990) An enlarged and updated internally Kushiro, I., Satake, H., and Akimoto, S. (1975) Carbonate-silicate reac- consistent thermodynamic dataset with uncertainties and correlations: tions at high pressures and possible presence of dolomite and magnesite

The system K2O-Na2O-CaO-MgO-MnO-FeO-Fe2O3-Al2O3-TiO2-SiO2- in the upper mantle. Earth and Planetary Science Letters, 28, 116±120.

C-H2-O2. Journal of Metamorphic Geology, 8, 89±124. MaÈder, U.K. and Berman, R.G. (1991) An equation of state for carbon (1991) A compensated-Redlich-Kwong (CORK) equation for vol- dioxide to high pressure and temperature. American Mineralogist, 76,

umes and fugacities of CO2 and H2O in the range 1 bar to 50 kbar and 1547±1559.

100±1600 degrees C. Contributions to Mineralogy and Petrology, 109, Newton, R.C. and Sharp, W.E. (1975) Stability of forsterite ϩ CO2 and

265±273. its bearing on the role of CO2 in the mantle. Earth and Planetary Science Irving, A.J. and Wyllie, P.J. (1975) Subsolidus and melting relationships Letters, 26, 239±244. Robie, R.A., Hemingway, B.S., and Fisher, J.R. (1978) Thermodynamic for calcite, magnesite and the join CaCO3-MgCO3 to 36 kb. Geochimica Cosmochimica Acta, 39, 35±53. properties of minerals and related substances at 298.15 K and 1 bar Jenkins, D.M., Newton, R.C., and Goldsmith, J.R. (1985) Relative stability (105 pascals) pressure and at higher temperatures. United States Geo- of Fe-free zoisite and clinozoisite. Journal of Geology, 93, 663±672. logical Survey Bulletin, 1452, 1±456. Johannes, W. (1969) An experimental investigation of the system MgO- Robie, R.A., Hemingway, B.S., and Takei, H. (1982) Heat capacities and entropies of Mg2SiO4,Mn2SiO4, and Co2SiO4 between 5 and 380 K. SiO2-H2O-CO2. American Journal of Science, 267, 1083±1104. Johannes, W. and Metz, P. (1968) Experimentelle Bestimmungen von American Mineralogist, 67, 470±482. Rosenbaum, J.M. and Slagel, M.M. (1995) C-O-H speciation in piston- Gleichgewichtsbeziehungen im System MgO-CO2-H2O. Neues Jahr- buch fuÈr Mineralogie Monatshefte, 15±26. cylinder experiments. American Mineralogist, 80, 109±114. Kerrick, D.M. and Jacobs, C.K. (1981) A modi®ed Redlich-Kwong equa- Saxena, S.K. and Fei, Y. (1987) High pressure and high temperature ¯uid fugacities. Geochimica et Cosmochimica Acta, 51, 783±791. tion for H2O, CO2, and H2O-CO2 mixtures at elevated pressures and temperatures. American Journal of Science, 281, 735±767. Shmulovich, K.I. and Shmonov, V.M. (1978) Tables of thermodynamic Koziol, A.M. and Newton, R.C. (1988) Redetermination of the anorthite properties of gases and liquids (carbon dioxide), 165 p. USSR Academy of Sciences, Moscow Bureau of Standards, Moscow. breakdown reaction and improvement of the plagioclase-garnet- Sterner, S.M. and Pitzer, K.S. (1994) An equation of state for carbon di- Al SiO -quartz geobarometer. American Mineralogist, 73, 216±223. 2 5 oxide valid from zero to extreme pressures. Contributions to Mineral- (1995) Experimental determination of the reactions magnesite ϩ ogy and Petrology, 117, 362±374. quartz ϭ enstatite ϩ CO and magnesite ϭ periclase ϩ CO and en- 2 2 Wang, A., Pasteris, J.D., Meyer, H.O.A., and Dele-Duboi, M.L. (1996) thalpies of formation of enstatite and magnesite. American Mineralo- Magnesite-bearing inclusion assemblage in natural diamond. Earth and gist, 80, 1252±1260. Planetary Science Letters, 141, 293±306. Krupka, K.M., Hemingway, B.S., Robie, R.A., and Kerrick, D.M. (1985a) Zhang, J., Martinez, I., Guyot, F., and Gillet, P. (1997) X-ray diffraction High-temperature heat capacities and derived thermodynamic properties study of magnesite at high pressure and high temperature. Physics and of anthophyllite, diopside, dolomite, enstatite, bronzite, talc, tremolite, Chemistry of Minerals, 24, 122±130. and wollastonite. American Mineralogist, 70, 261±271. Krupka, K.M., Robie, R.A., Hemingway, B.S., Kerrick, D.M., and Ito, J. MANUSCRIPT RECEIVED MARCH 3, 1997 (1985b) Low-temperature heat capacities and derived thermodynamic MANUSCRIPT ACCEPTED NOVEMBER 5, 1997